In a DIC the complexity of the model is estimated during the MCMC process. Say you are estimating a random effects model with 50 schools - the nominal degrees of freedom consumed by these 50 differentials is 50 but if you assume that they come from a distribution with a common variance the df consumed will be typically somewhat less than that . The DIC is the badness of fit penalized by complexity - complexity (pD as it is known is the estimated degrees of freedom consumed in the fit in the model.